Yvette has calculated that it will take her team exactly three hours to check 16 chapters of a report. She has already allocated each person two chapters. It will take either \(30,40,45,45,50,55,70\) or 80 minutes to check each of the remaining chapters. To which person should Yvette allocate the chapter that will take 40 minutes? \begin{tabular}{ccccc} & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ Jack & 40 & 40 & & \\ Romano & 25 & 35 & \\ Eille & 40 & 60 & \\ Pat & 30 & 45 & \\ Select one: Ellie Jack Romano Pat

To solve this problem, we need to allocate the chapter that takes 40 minutes to one of the four team members: Jack, Romano, Ellie, or Pat. The goal is to assign the task so that the workload is balanced, and no one exceeds the total time available.

**Step 1: Analyze the current allocations.**

The initial allocations given in the problem are:

- **Jack:** 40 minutes + 40 minutes = 80 minutes
- **Romano:** 25 minutes + 35 minutes = 60 minutes
- **Ellie:** 40 minutes + 60 minutes = 100 minutes
- **Pat:** 30 minutes + 45 minutes = 75 minutes

**Step 2: Consider the additional chapter (40 minutes) allocation.**

Now, let's analyze how assigning the 40-minute chapter to each person would affect their total time:

- **Jack:** \( 80 + 40 = 120 \) minutes
- **Romano:** \( 60 + 40 = 100 \) minutes
- **Ellie:** \( 100 + 40 = 140 \) minutes
- **Pat:** \( 75 + 40 = 115 \) minutes

**Step 3: Choose the optimal assignment.**

Yvette wants to allocate the chapter such that the time is balanced among the team members and no one is overburdened.

- If we give the chapter to **Jack**, his total time becomes 120 minutes.
- If we give the chapter to **Romano**, his total time becomes 100 minutes.
- If we give the chapter to **Ellie**, her total time becomes 140 minutes.
- If we give the chapter to **Pat**, his total time becomes 115 minutes.

The most balanced option that keeps the times as close as possible is assigning the 40-minute chapter to **Romano**.

**Conclusion:**
Yvette should allocate the chapter that will take 40 minutes to **Romano**.

---

Would you like further details or have any questions about this solution? 

Here are some related questions to deepen your understanding:
1. What would happen if a different time were assigned to each member?
2. How could you distribute all the remaining times to achieve the most balanced workload?
3. How do you calculate the total time for each person given the additional chapters?
4. How would the answer change if each chapter took a different amount of time?
5. How does the concept of optimization apply in this scenario?
6. What is the importance of balancing workloads in team tasks?
7. How would adding more team members affect the allocation?
8. Can you think of any other factors Yvette should consider when making her decision?

**Tip:** Balancing workloads is key in team tasks to ensure efficiency and fairness.

Explore a math problem involving optimal time allocation among team members. Yvette needs to allocate a 40-minute task to Jack, Romano, Ellie, or Pat without overburdening any team member. Discover the balanced approach to task assignment and its implications.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation